No. The nature of the lithium battery chemistry does not require periodic cycling to maintain capacity.
Furthermore, the periodic cycling described in the apple documents listed above (@I-M-JM's Post) does not have an effect on the battery chemistry. It only serves to allow the battery capacity meter to accurately track the battery capacity.
Periodically draining the battery only serves to allow the Battery metering systems to accurately estimate the remaining battery capacity. It is not needed to maintain the battery itself, and actually wastes a battery cycle.
Basically, if you don't run your battery down for a long time, the next time you disconnect the laptop from AC, the estimated time renaming value will be incorrect. However, the actually battery capacity and runtime will be unchanged from normal.
The statement "For proper maintenance of a lithium-based battery, it’s important to keep the electrons in it moving occasionally." from Apple's site is actually incorrect regarding the lithium battery chemistry at worst, and an oversimplification at best.
Furthermore, The battery metering and battery charging systems are separate, so inaccuracies in the battery metering system will not cause errors in charging the battery (before you ask). Lithium cells are actually quite simple to charge.